The boundary between basins of attraction, i.e. between two zones of stability of different characteristics.
R.H. ABRAHAM and C.D. SHAW state: "By definition, separatrix points are not in basins. Thus, they belong to the insets of limit sets which are not attractors, the exceptional limit sets" (1987, p.549).
As a result, the separatrix corresponds to the critical threshold, the locus where bifurcations can take place.
As stated by St. KAUFFMAN, in two dimensions, the separatrix is a line (i.e. one-dimensional), and in three dimensions it is a surface (i.e. bi-dimensional) (1993, p.176-7).
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Bertalanffy Center for the Study of Systems Science (2020). Title of the entry. In Charles François (Ed.), International Encyclopedia of Systems and Cybernetics (2). Retrieved from www.systemspedia.org/[full/url]
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